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Math Help - Poisson distribution help

  1. #1
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    Poisson distribution help

    Question is :

    5. Write down the probability distribution of a Poisson random variable with
    parameter  \mu
    The average number of earthquakes in a certain region is 2 per week. Assume
    that, in any time interval, the number of earthquakes occurring has a Poisson
    distribution, calculate
    (i) the probability of no earthquakes in a given week;
    (ii) the probability of at least 1 earthquake in a given week;
    (iii) the probability of at least 3 earthquakes in a given fortnight.
    (iv) Calculate the probability that the time until the next earthquake, starting from now, is at least 1 week.

    I need help on part (iv) my answers for the others parts are :

    i) P(x=o) (e^-2 x 2^0)/0! =0.1353
    ii) P(x\geq1) =1-P(x\leq0)<br />
1-0.1353=0.8647
    iii)  P(x\geq3)=1-P(x\leq2)
     p(x\leq2)=P(x=0)+p(x=1)+p(x=2) =<br />
1-P(x\leq2)=0.3233

    these are my answers.

    can someone please help me on part (iv)

    thanks
    Last edited by mr fantastic; May 25th 2009 at 07:38 PM. Reason: Fixed latex
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  2. #2
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    Quote Originally Posted by master_2m8 View Post
    Question is :

    5. Write down the probability distribution of a Poisson random variable with
    parameter \mu
    The average number of earthquakes in a certain region is 2 per week. Assume
    that, in any time interval, the number of earthquakes occurring has a Poisson
    distribution, calculate
    (i) the probability of no earthquakes in a given week;
    (ii) the probability of at least 1 earthquake in a given week;
    (iii) the probability of at least 3 earthquakes in a given fortnight.
    (iv) Calculate the probability that the time until the next earthquake, starting from now, is at least 1 week.

    I need help on part (iv) my answers for the others parts are :

    i) P(x=o) (e^-2 x 2^0)/0! =0.1353
    ii) P(x\geq1) =1-P(x\leq 0)<br />
\Rightarrow 1-0.1353 =0.8647
    iii)  P(x\geq3)=1-P(x\leq2)
     p(x\leq2)=P(x=0)+p(x=1)+p(x=2) =<br />
1-P(x\leq2)=0.3233

    these are my answers.

    can someone please help me on part (iv)

    thanks
    Read part 3 here: Poisson process - Wikipedia, the free encyclopedia
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